The transpiration cooled first wall and blanket concept

Fusion Engineering and Design 61 /62 (2002) 477 /482 www.elsevier.com/locate/fusengdes

The transpiration cooled first wall and blanket concept Leopold Barleon 1,
, Clement Wong General Atomics, P.O. Box 85608, San Diego, CA 92186-5608, USA

Abstract To achieve high thermal performance at high power density the EVOLVE concept was investigated under the APEX program. The EVOLVE W-alloy first wall and blanket concept proposes to use transpiration cooling of the first wall and boiling or vaporizing lithium (Li) in the blanket zone. Critical issues of this concept are: the Magnetohydrodynamic (MHD) pressure losses of the Li circuit, the evaporation through a capillary structure and the needed superheating of the Li at the first wall and blanket zones. Application of the transpiration concept to the blanket region results in the integrated transpiration cooling concept (ITCC) with either toroidal or poloidal first wall channels. For both orientations the routing of the liquid Li and the Li vapor has been modeled and the corresponding pressure losses have been calculated by varying the width of the supplying slot and the capillary diameter. The concept works when the sum of the active and passive pumping head is higher than the total system pressure losses and when the temperature at the inner side of the first wall does not override the superheating limit of the coolant. This cooling concept has been extended to the divertor design, and the removal of a surface heat flux of up to 10 MW/m2 appears to be possible, but this paper will focus on the transpiration cooled first wall and blanket concept assessment. Published by Elsevier Science B.V. Keywords: Blanket concept; EVOLVE concept; Integrated transpiration cooling concept (ITCC)

1. Introduction In designing liquid metal (LM), cooled blankets of a fusion reactor with magnetically confined plasma, one has to deal with two special features: . high peak heat load at the first wall (FW), and the;


Corresponding author. Tel.: /1-858-455-4258; fax: /1858-455-2838 E-mail address: [email protected] (L. Barleon). 1 Consultant to General Atomics. 0920-3796/02/$ - see front matter. Published by Elsevier Science B.V. PII: S 0 9 2 0 - 3 7 9 6 ( 0 2 ) 0 0 2 9 3 - 4

. magnetohydrodynamic (MHD) effect of circulating LM coolants in a magnetic field. In order to avoid the conflicting requirements of high coolant velocity for good heat transfer and low coolant velocity for low MHD pressure losses an evaporation cooling of the FW using capillary cooling was proposed [1] taking advantage of the high value of the heat of vaporization. This cooling concept has been extended to the divertor design [2]. Depending on the superheating limit of the Li at the plasma facing wall of the divertor, the removal of a surface heat flux of up to 10 MW/m2 appears to be possible. For this paper, we are

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going to focus on the assessment of the transpiration cooled FW and blanket concept.

the tube is given by B
/BP cos a , where the poloidal field BP is approximated by 1/10 BT. 2.1. The pressure balance

2. Modeling and analysis of the toroidal first wall cooling Fig. 1 shows schematically the original EVOLVE concept with the capillary cooled FW and the tray, which is cooled by pool boiling. The cross section of the toroidally oriented FW tubes is shown. The annular gap is filled with Li, which is transported to the capillaries. The figure shows the separate functions of feeding, pumping and evaporation of Li. The Li is fed through an azimuthal gap of width w and evaporated and pumped in a capillary of diameter dc. For the analysis, the following assumptions and approximations are made: the toroidal field BT is exactly aligned with the tube, the magnetic field perpendicular to

In order to keep the Li mass balance between the Li evaporated in the capillary and the Li fed from the sump, the capillary pumping pressure DPC has always to be higher than the sum of all pressure losses of the Li along its flow path. This forms the limiting condition for the design as shown in the following equation. DpC ]DpH1 DpH2 DpH3 DpM1 DpM2 DpM3 (1)

DpLV ;

where DpC is the capillary pressure head; DpH1 is the hydrostatic pressure head of the liquid; DpH2 is the feeding gap liquid pressure drop; DpH3 is the pressure drop of the liquid in the capillary; DpM1 is the MHD pressure drop in the feeding gap due to the poloidal field; DpM2 is the MHD pressure drop in the feeding gap due to the toroidal field; DpM3 is the MHD pressure drop in the capillary due to the toroidal field and DpLV is the pressure jump through the evaporation surface. For the thermohydraulic calculations of the FW channel an effective heat flux at the FW was used, which takes into account the surface heat flux and the heat flux generated by volumetric heating of the FW and the Li within the feeding gap. The modeling and calculations of the different hydrodynamic pressure losses are based on standard correlations [3]. The modeling of the dominating MHD pressure losses is described in the APEX project report [4]. The most important terms are the capillary pressure head and the maximally allowed superheat of the Li at the FW, which will be described in the following. 2.2. Capillary pressure head The hemispherical shape of the surface of a liquid in a capillary causes a pressure difference across the surface and can be written as [3].

Fig. 1. Schematic of the cross section through the toroidal FWcooling channel.

DpC 

2ssLi cos u r

(Pa):

(2)

L. Barleon, C. Wong / Fusion Engineering and Design 61 /62 (2002) 477 /482

where ssLi is the surface tension of the liquid Li at the saturation temperature, u is the contact angle of the wetting Li, and r /dc/2 is the radius of the capillary. At temperatures above 900 8C, Li wets the tungsten structures completely and the contact angle u tends to zero and the cos u /1.

2.3. Superheating of Li at FW The maximum allowed superheating temperature of a heated liquid at a wall of a roughness d is a subject in many text books, e.g. J.M. Delhaye [5]. Furthermore, the superheating of liquid sodium at a heated wall, heterogeneous nucleation, was one of the key issues under the LM Fast Breeder Reactor (LMFBR) research and extensive literature is compiled by Kottowski /Duemenil [6]. Superheat of sodium up to 200 8C was reported but it was also shown that it is very difficult to reproduce these high values. This is due to the fact that the incipient boiling superheat is affected by many parameters; for example; gas content of the LM, gas trapped in the pockets of the wall cavities (roughness), oxide impurity of the LM, pressure/ temperature history, heating surface condition, velocity of the LM, nuclear radiation, and heat flux. It should be noted that for capillary cooling, we want to have high superheat. Therefore, the main question was how fast the roughness of the heated surface is activated by the gas dissolved in the LM and how high is the superheat after this gas is absorbed onto the metal surface. For power reactors, we should have an extensive outgasing procedure and would also be operating at high temperature during power production operation. Therefore, the probability of gas filled pockets acting as nucleation centers on the metallic surface would will be very low. However, at this time, no reliable data on the superheat of Li under such conditions could be found in the literature. Accordingly, we used the following Eq. (3), which describes the DTSuperheat as a function of surface roughness, d , as a conservative approach.

DTSuperheat 

3:06ssLi TS rv;Li HLi d

;

479

(3)

where d is the standard depth of a rough surface. For a rather smooth surface with d /25 /10 6 m and TS /1473 K, we get a superheat of DTSuperheat /104 K. Actually, the situation may be more favorable. Dalle Donne [7,8] has shown that, with normal smooth stainless steel surfaces in the presence of fully wetting LMs, the largest surface cavity with an opening radius of about 0.25 mm was still filled with vapor without initiating nucleation or gas after a long time in contact with the liquid. In our case with smooth tungsten surfaces and long time exposure a similar behavior can be expected. Using the method developed by Dalle Donne [7], for an opening radius of 1 m and a saturation temperature of TS /1500 K, we get a superheating of 350 K, corresponding to a wall surface temperature of 1850 K. 2.4. First wall toroidal channel modeling For further assessment, we modeled all the MHD and thermohydraulic pressure losses. Calculations are done with the MATHCAD 2000 [9] software and material data are from Vargaftik [10] and Kirillin [11]. Key parameters are given in Table 1. Fig. 2 shows the dependence of the capillary pressure head as a function of the Table 1 Key input parameters Parameters common for toroidal and poloidal Fw channels Surface heat flux q0ƒ (MW/m2) Toroidal magnetic field strength, BT (T) Wall thickness, tw (m) Thickness of the capillary structure, tc (m) Area fraction of the capillaries, bc Thickness of porous tungsten sheet, tWR (m) Porosity of the tungsten sheet, o Sh

2.0 6.0 3.0E-3 0.5E-3 0.5 2.0E-3 0.5

Toroidal FW channels Outer tube radius, rH (m) Tube length, lHR (m) Toroidal distance of the spacers, bt (m) Effective thickness of the spacers, tWT (m)

0.05 3.00 0.04 0.5E-3

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Table 2 Key results of the toroidal first wall channel transpiration cooling

Fig. 2. Capillary pressure head and the total pressure drop as a function of capillary diameter dc and FW feeding gap width w , respectively, for BT /6 and 10 T and for toroidal spacer thickness of 0.2 and 0.5 mm.

capillary diameter dc and the total pressure drop of the liquid Li needed to remove a heat flux of q0ƒ /2 MW/m2 from the FW as a function of gap width, w. The contributions of the different pressure drops are taken at an angle a where the total pressure drop Dptotal has its maximum value. The calculations of the MHD pressure drop are conducted neglecting three-dimensional effects, which may happen due to the changing magnetic field strength and/or mass flow in the feeding gap along the flow direction. Results for a fixed set of the toroidal FW channel parameters are given in Table 2.

FW feeding gap width, w (mm) Effective heat flux at the FW (MW/m2) Total pressure drop (Pa) Necessary capillary diameter (mm) Temperature increase across the gap (K) Temperature at the FW (K) Temperature at the outside of the FW (K) Theoretical limit of superheat (K) The true superheat (K) Vapor mass flow rate at the tube outlet (kg/s) Vapor velocity at the outlet (m/s)a Pressure loss along the tube (Pa) Integrated FW channel mass flow rate (kg/s) Needed manifold diameter (m)b

1.0 2.5 2.27E/3 0.43 52.6 1526 1614 103 65.9 0.035 241 179 2.837 0.68

a Reduction of vapor area by the feeding tube not considered. b For a limited vapor velocity of 400 m/s.

Fig. 3 shows a schematic of this concept including the routing of the liquid Li from the tray to the FW and of the vapor generated in these regions. The thin, 0.5 mm thick porous wall has a separation of w /0.8 mm on the inner side of the FW. In the blanket region, porous sheets (2 mm thick) are used everywhere to insure transpiration cooling of the blanket Li and the Li in the feed ducts supplying the FW channels. The width of the liquid Li slabs of the blanket is defined by the allowable superheat at the centerline while balancing the volumetric heating in the lithium and cooling by the capillaries. For the case considered a DTSH /100 K was assumed. 3.1. Basic features of transpiration cooling

3. The integrated transpiration cooling concept In the poloidal FW cooling channel concept an integrated transpiration cooling concept (ITCC) was proposed by removing not only the power generated from the FW but also the volumetric power generated from the blanket. It is also an extension of the transpiration cooled FW concept. The lithium in the blanket confined by porous walls also forms the supply of lithium to the FW. Additionally the fluid height in the tray is used to support the passive capillary pumping.

For the ITCC blanket concept the basic features described below were observed. Avoid any boiling, use only evaporation cooling through free porous surfaces and take advantage of the high superheat capability of volumetrically heated pure Li (up to 200 K) in the breeding zone. All liquid Li slab and feeding slots are to be cooled by evaporation cooling through porous walls. Keep the MHD pressure losses of the liquid Li in feeding channels by proper design as low as possible. We have to minimize the thickness of the porous walls of the

L. Barleon, C. Wong / Fusion Engineering and Design 61 /62 (2002) 477 /482

w(R)2

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2DTmax lLi q?ƒ(R)

respectively:

481

(5)

where R is radial location in the blanket; DTmax is the maximal temperature in the slab; DTmax 5/ DTSuperheat; lLi is the heat conductivity of Li, and q???(R ), is the averaged volumetric power density. The surface capillary size has to be selected corresponding to the pumping needs. The Li filled porous walls also have to be taken into account in calculating the thickness of the feeding gaps and the Li-slots using an averaged volumetric power density and an effective heat conductivity keff of these walls. For the calculations the same basic equations as given in Section 2 can be used. More details are given in [4]. Fig. 4 shows the integral pressure drop and the capillary pressure head as a function of the FW feeding gap width w and of the capillary diameter dc, respectively, for a toroidal field component BT /6 T and for radial feeding gap thickness 5, 7.5 and 10 mm.

4. Conclusion Based on the EVOLVE concept, we evaluated the performance of the transpiration cooled FW. The concept was then extended to the ITCC for the poloidally oriented FW channel design. Analytical tools were developed for detailed evaluaFig. 3. The ITCC with poloidal oriented FW channels.

breeding zone, keep the applied pressure at any position in the system below the break-through pressure of the capillary surfaces, and optimize the width of the vapor channels with respect to pressure drop and void fraction. Depending on whether the feeding slot is cooled only from one side or from both sides, the width of the feeding slots has to fulfill the following condition. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2DTmax lLi w(R) (4) q?ƒ(R) or,

Fig. 4. ITCC with poloidal FW channels.

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tion. The results of the modeled calculations show that the transpiration cooling of the FW is feasible. The ITCC concepts are also credible. The concept works when the active and passive pumping head is higher than the total system pressure losses, and when the temperature at the inner side of the FW does not override the superheating limit of the Li coolant. Different MHD effects due to the magnetic field and the pressure jump across the evaporation surface dominates the pressure losses. The higher theoretically predicted allowable superheating at the FW up to 350 K could be used to extend either the safety margin to maintain stable transpiration cooling or allow much higher surface heat loads capability, which is required in the capillary cooling of the high heat loads at the divertor.

Acknowledgements Work supported by US Department of Energy under Contract No. DE-AC03-98ER54411. Authors wish to thank Dr S. Malang of FZK for his technical advice.

References [1] M.A. Abdou, et al., APEX Interim Report, November 1999, UCLA-ENG-99-206, UCLA-FNT-107. [2] J. Reimann, L. Barleon, L. Boccacini, S. Malang, Conceptual Design of an Evaporation-cooled Liquid Metal Divertor for Fusion Power Plants, Symposium on Fusion Technology (SOFT), Lisbon, 2000. [3] P.D. Dunn, D.A. Reay, Heat Pipes, fourth ed., Pergamon, 1994. [4] L. Barleon, C. Wong et al., Evolution of a Transpiration Cooled FW and Blanket Concept, to be published in APEX project website. [5] J.M. Delhaye, M. Giot, M.L. Riethmueller, (Eds.), Thermohydraulics of Two-Phase Systems for Industrial Design and Nuclear Engineering, Hemisphere Publishing Company. [6] X. Xaa, in: H.M. Kottowski-Duemenil (Ed.), Liquid Metal Thermohydraulics, INFORUM-Verlag, 1977. [7] M. Dalle Donne, A new and simple method of estimating the liquid superheat due to surface conditions in nucleate boiling and its application to sodium, Nukleonik, 8. Band 3. Heft, 1966, s. 133 /137. [8] M. Dalle Donne, M.P. Ferranti, The growth of vapor bubbles in superheated sodium, Int. J. Heat Mass Transfer 18 (1975) 477 /493. [9] MATHCAD, MathSoft, Inc., 101 Main Street, Massachusetts 02142, USA, http://www.mathsoft.com. [10] N.B. Vargaftik, Tables on the Thermophysical Properties of Liquids and Gases, second ed., Hemisphere Publishing Corporation, 1975. [11] V.A. Kirillin (Ed.), Liquid-Metal Coolants for Heat Pipes and Power Plants, Hemisphere Publishing Corp., 1990.